Froude Number Calculator

Calculator

Solve for

Switch between finding Fr, V, or L.

Application context

Controls interpretation text, not the formula.

Precision (decimals)

Choose 0–12 decimals for display.

Velocity, V

Required when solving for Fr or L.

Characteristic length, L

Use depth, diameter, or a representative length.

Gravity, g

Earth standard is 9.80665 m/s².

Froude number, Fr

Required when solving for V or L.

Reset

Tip: choose a representative length for your problem. In open channels, hydraulic depth is common. For ships, waterline length is often used.

Core definition

Fr = V / √(gL)

Where V is the characteristic velocity, g is gravitational acceleration, and L is a characteristic length scale.

Rearranged forms

V = Fr · √(gL)
L = V² / (g · Fr²)

Select what you want to solve for: Fr, V, or L.
Enter the required inputs and pick units for each value.
Keep gravity positive and use a representative length scale.
Press Calculate to view results above the form.
Use Download CSV or Download PDF for reports.

Case	V (m/s)	L (m)	g (m/s²)	Fr	Typical note
Open channel	1.20	0.60	9.80665	0.49	Subcritical flow tendency
Critical condition	2.43	0.60	9.80665	1.00	Transition at critical flow
Fast flow	4.00	0.40	9.80665	2.02	Supercritical behavior
Marine scaling	10.0	50.0	9.80665	0.45	Displacement-range estimate

Examples are illustrative; choose L to match your definition.

1) What the number compares

Froude number compares inertial motion to gravity-wave response using √(gL). It is dimensionless, making it useful for comparing systems with different units and sizes. You can view it as Fr = V/c, where c = √(gL) is a gravity wave speed scale. It is central for free-surface flows, spillways, hydraulic structures, and ship motion.

2) Picking the right length scale

The length L must reflect your geometry. In open channels, use flow depth or hydraulic depth (area divided by top width). For ships, waterline length is common. Using an inconsistent L can shift Fr and distort comparisons.

3) Open-channel regimes

For open-channel flow, Fr < 1 is subcritical, so surface disturbances can influence upstream. Fr ≈ 1 is critical and often occurs at controls like weirs or flumes. Fr > 1 is supercritical, where upstream influence is limited and jumps can form.

4) Typical values for checking inputs

Many canals and rivers fall around Fr = 0.1 to 0.8. Supercritical chutes and spillways can exceed Fr = 2. In marine scaling, displacement ships often operate near Fr ≈ 0.2 to 0.4, while higher values can signal strong wave-making. Use ranges as plausibility checks.

5) Similarity in physical modeling

When gravity and free-surface waves dominate, matching Fr between model and prototype improves similarity. With geometric scale ratio λ, velocity scales with √λ and characteristic time scales with √λ. This guides model test speeds and how quickly wave features develop. Reynolds number may not match simultaneously, so viscosity effects should be reviewed separately.

6) Units and gravity sensitivity

This tool converts your selected units to SI internally, then reports results back in chosen units. Gravity defaults to 9.80665 m/s² but can be changed for sensitivity studies. Because √(gL) grows with L, small length errors can noticeably change Fr.

7) Interpreting results for decisions

Use Fr with other indicators. In channels, it helps anticipate jump likelihood, energy dissipation needs, and control behavior. For ships, it supports wave-resistance comparisons across sizes. Pair Fr with Reynolds number and roughness to judge turbulence and boundary effects. Treat the regime note as guidance, then confirm with geometry and measured depth or draft.

8) Quick numerical check

Try V = 2.43 m/s, L = 0.60 m, and g = 9.80665 m/s². The calculator returns √(gL) ≈ 2.43 m/s and Fr ≈ 1.00, indicating critical conditions. Doubling V with the same L moves Fr near 2.00.

1) What should I use for the characteristic length L?

Use a length that represents the free-surface wave scale. Depth or hydraulic depth works for channels, while waterline length is common for ships. Keep the definition consistent across comparisons.

2) Does the context selection change the calculation?

No. The formula stays the same. Context only adjusts interpretation text so you can read Fr as a regime indicator for channels or a scaling indicator for marine and general hydraulics.

3) Why is Fr near 1 called critical?

At Fr ≈ 1, velocity matches the gravity-wave speed scale. The flow becomes sensitive to controls and geometry, and disturbances do not clearly travel upstream or downstream.

4) Can I solve for velocity from Fr and L?

Yes. Select “Velocity (V)” and enter Fr, L, and g. The calculator uses V = Fr·√(gL) and reports V in your selected velocity units.

5) Are the typical ranges strict limits?

No. They are common engineering ranges. Natural channels and vessels can vary widely. Use ranges to sanity-check inputs, then rely on measurements and design criteria.

6) What is the effect of changing gravity g?

Increasing g increases √(gL), which lowers Fr for the same V and L. This is useful for sensitivity checks or comparing conditions under different gravitational environments.

7) Is a larger Froude number always desirable?

Not always. High Fr can indicate energetic supercritical flow and jump risk in channels, or stronger wave-making in marine applications. Suitability depends on stability, efficiency, and design goals.